Partial Differential Equations Solution Manual
© Leon van Dommelen
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1.1 Basic Concepts
1
. Introduction
Subsections
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Basic Concepts
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The prevalence of partial differential equations
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Definitions
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Typical boundary conditions
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The Standard Examples
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The Laplace equation
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Solution stanexl-a
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Solution stanexl-b
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Solution stanexl-b1
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Solution stanexl-b2
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Solution stanexl-b3
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Solution stanexl-b5
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Solution stanexl-c
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Solution stanexl-d
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Solution stanexl-e
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The heat equation
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Solution stanexh-a
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Solution stanexh-b
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The wave equation
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Solution stanexw-a
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Solution stanexw-b
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Solution stanexw-c
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Solution stanexw-e
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Solution stanexw-f
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Classification
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Introduction
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Scalar second order equations
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Solution clasnd-a
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Changes of Coordinates
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Introduction
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The formulae for coordinate transformations
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Rotation of coordinates
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Solution rotcoor-a
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Explanation of the classification
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Solution expclass-a
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Two-Dimensional Coordinate Transforms
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Characteristic Coordinates
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Parabolic equations in two dimensions
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Elliptic equations in two dimensions
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Solution 2dcanel-a
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Properly Posedness
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The conditions for properly posedness
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Solution ppc-a
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Solution ppc-b
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Solution ppc-c
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An improperly posed parabolic problem
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An improperly posed elliptic problem
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Solution ppe-a
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Solution ppe-b
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Solution ppe-c
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Solution ppe-d
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Solution ppe-e
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Solution ppe-f
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Improperly posed hyperbolic problems
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Solution pph-a
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Solution pph-b
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Energy methods
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The Poisson equation
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Solution emp-a
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Solution emp-b
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The heat equation
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The wave equation
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Variational methods [None]
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1.1 Basic Concepts
FAMU-FSU College of Engineering
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